Questions tagged [integer]

For challenges involving the manipulation of integers.

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13 votes
10 answers
901 views

Carryless factors

Carryless multiplication is an operation similar to binary long multiplication, but with XOR instead of addition: ...
19 votes
25 answers
1k views

Carry-less sum given a base b

Given a list of positive integers \$\mathcal I=I_1,I_2,I_3,...,I_n\$ and a base \$b>1\$ return their "carry-less sum", i.e. represent \$\mathcal I\$ in base \$b\$ and sum digit-by-digit ...
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1 vote
5 answers
204 views

Find number components with lowest distribution

Let us assume that we have number X. Let us assume that we have positive integer "components" (C) of this ...
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18 votes
9 answers
1k views

Cryptic Multiplications

Given two non-negative integers e.g. 27, 96 their multiplication expression would be 27 x 96 = 2592. If now each digits is ...
  • 2,153
19 votes
39 answers
2k views

Shifted auto-sum

Let’s take a positive integer such as 123. We define the shifted auto-sum of this integer as follows: 123 has 3 digits. We thus consider 3 copies of 123. We stack ...
  • 36.8k
13 votes
6 answers
796 views

Exponential transform of an integer sequence

The exponential generating function (e.g.f.) of a sequence \$a_n\$ is defined as the formal power series \$f(x) = \sum_{n=0}^{\infty} \frac{a_n}{n!} x^n\$. When \$a_0 = 0\$, we can apply the ...
  • 37.4k
23 votes
25 answers
3k views

How far from binary?

Given a decimal integer n as input, output the smallest (in terms of absolute value) decimal integer m such that the absolute ...
  • 36.8k
7 votes
24 answers
2k views

Find the nth Fibonacci number, where n is the mth Fibonacci number

Introduction If \$\newcommand{\fib}{\operatorname{fib}}\fib(x)\$ calculates the \$x\$th Fibonacci number, write a program that calculates \$\fib(\fib(m))\$ for any integer value of \$m \ge 0\$. (Of ...
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8 votes
5 answers
887 views

Spell out an integer... in NDos' way

Objective Given a positive integer, spell it out in the conlang I made. Specification Let \$n\$ be the inputted integer. \$n\$ shall be spelled out in the following specification. The entire spelling ...
  • 4,173
19 votes
6 answers
2k views

Is it 1089-able?

\$ 1089 \$ is a very special number. To prove why, select any 3-digit number whose first and last digits differ by at least 2. Then, reverse the digits, and take the difference of these two numbers. ...
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10 votes
11 answers
1k views

Smallest numbers whose square has even number of digits

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  • 9,806
13 votes
17 answers
1k views

The interstice of two binary numbers

Given two integers, compute the two numbers that come from the blending the bits of the binary numbers of equal length(same number of digits, a number with less digits has zeros added), one after the ...
  • 420
21 votes
26 answers
2k views

Randomly Rounding

Input a decimal number and round it to an integer, randomly rounding up or down with a probability based on its fractional part, so the expected value of the output equals to the input value. If ...
  • 30.8k
4 votes
19 answers
554 views

Double bit rotation to the right [closed]

Given a positive integer as input, output that integer, but with its bits rotated two times to the right. Also, think of the number as a donut of bits, eg. ...
  • 373
12 votes
3 answers
277 views

Line Islands in a Word Search

My third word search related challenge in a row. :) Challenge: Brief explanation of what a word search is: In a word search you'll be given a grid of letters and a list of words. The idea is to cross ...
4 votes
3 answers
261 views

Find All Digitroot Cyclic Sequences With Length Greater Than One

Digital sum, DR, Digit root is the iterative process of summing digits of a number until you end up with a single digit root number: e.g. digit root of 12345 is 6 since 1 + 2 + 3 + 4 + 5 = 15 = 1+5. ...
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29 votes
16 answers
2k views

How-many-bonacci-like is this sequence?

Inspired by @emanresu A's Is it a fibonacci-like sequence? Make sure to upvote that challenge as well! We say a sequence is Fibonacci-like, if, starting from the third term (\$1\$-indexed), each term ...
  • 37.4k
10 votes
3 answers
306 views

Coordinates for a Heronian tetrahedron

Did you know that Heronian Tetrahedra Are Lattice Tetrahedra? A Heronian tetrahedron is a tetrahedron where the length of each edge is an integer, the area of each face is an integer, and the volume ...
  • 8,117
16 votes
26 answers
1k views

Sum of the first n elements of the sequence of 9's complement

Let's consider the following sequence: $$9,8,7,6,5,4,3,2,1,0,89,88,87,86,85,84,83,82,81,80,79,78,77,76,75,74,73,72,71...$$ This is the sequence of \$9\$'s complement of a number: that is, \$ a(x) = 10^...
  • 1,805
14 votes
15 answers
1k views

How many blocks make a "truncated square-pyramid garden"?

A truncated square-pyramid of height \$h\$ has \$h\$ square layers where each layer has a side \$1\$ greater than the one above it, apart from the top layer which is a square of blocks with a given ...
32 votes
35 answers
3k views

Is it a fibonacci-like sequence?

The Fibonacci Sequence is a sequence of positive integers where the first two elements are 1 and the rest are the sum of the previous two. It begins \$1, 1, 2, 3, 5, 8, 13\$ and continues forever. But ...
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21 votes
21 answers
1k views

Is given number a concat of two squares

Given a positive integer, determine if it can be represented as a concatenation of two square numbers. Concatenated numbers may not begin with 0 (except for 0). Any leading zeros in input should be ...
  • 237
18 votes
27 answers
2k views

Prime a*b+c of N

Given an integer \$N\$, print or return integers \$a\$, \$b\$, and \$c\$ that satisfy all of the following conditions, if such integers exist: \$a \times b + c = N\$ \$a\$, \$b\$, and \$c\$ are all ...
  • 727
6 votes
1 answer
194 views

Represent any integer with an expression that uses no digit besides '4' [closed]

Fourward (Introduction) I have an unhealthy obsession with the number 4. I love it so much, in fact, that seeing any other digit is frustrating to me. I therefour wish to create a 'Fourier ...
10 votes
6 answers
480 views

Mirror an integer... in NDos' way

NDos' Numeral System NDos' numeral system is a numeral system invented by me. It represents every nonnegative integer by a binary tree. Given a nonnegative integer \$n\$: If \$n=0\$, it is ...
  • 4,173
16 votes
15 answers
1k views

Encode integers with some others

Input a non-empty array of positive (greater than 0) integers. Output another non-empty array of positive integers which encode the input array. Output array does not use any numbers used in the input ...
  • 30.8k
25 votes
33 answers
2k views

Even sum subarrays

Given an array of integers, count the number of contiguous subarrays with an even sum. You may assume that the array is non-empty, and contains only non-negative integers. This is code-golf, so the ...
  • 18.6k
18 votes
6 answers
750 views

Is it an elementary matrix?

Consider a linear system of equations, in \$n\$ unknowns, expressed as $$A \textbf x = \textbf b$$ where \$A \in M_{n,n}(\mathbb Z)\$ is an \$n \times n\$ matrix of integers, \$\textbf x\$ is a column ...
13 votes
9 answers
998 views

Bijective meets mixed base

Background A bijective base \$b\$ numeration, where \$b\$ is a positive integer, is a bijective positional notation that makes use of \$b\$ symbols with associated values of \$1,2,\cdots,b\$. ...
  • 66.1k
11 votes
2 answers
424 views

Branchless (MIPS) assembly code for median of 3

I was trying to write a short MIPS32 code for computing the median of three registers. The rules: Assume that some values are pre-loaded into $t0, ...
  • 211
14 votes
12 answers
1k views

Nega-Zeckendorf representation

Background Zeckendorf representation is a numeral system where each digit has the value of Fibonacci numbers (1, 2, 3, 5, 8, 13, ...) and no two consecutive digits can be 1. Nega-Zeckendorf ...
  • 66.1k
24 votes
18 answers
2k views

Double trace of a square matrix

Inspired by a question (now closed) at Stack Overflow. Given a square matrix, let its double trace be defined as the sum of the entries from its main diagonal and its anti-diagonal. These are marked ...
  • 100k
21 votes
9 answers
1k views

Self-referential triangle sequence

Output the flattened version of the sequence A297359, which starts like the following: ...
  • 66.1k
28 votes
48 answers
3k views

Swap Two Values in a List

Introduction: Although we have a lot of challenges where swapping two items in a list is a subtask, like Single swaps of an array; Swap to Sort an Array; \$n\$ swaps into a nop; etc., we don't have ...
16 votes
7 answers
877 views

Maybe fractal sequence?

Background A fractal sequence (Wikipedia; MathWorld) is an infinite sequence of positive integers meeting the following conditions: Each positive integer appears infinitely many times in the sequence....
  • 66.1k
20 votes
12 answers
1k views

Minimally prepend numbers to get a symmetric Young diagram

Background A Young diagram is a diagram that represents a nonincreasing sequence of positive integers using left-justified rows of squares. As an example, 5, 4, 1 ...
  • 66.1k
24 votes
31 answers
3k views

"-rot" transform

Background -rot transform (read as "minus-rot transform") is a sequence transformation I just invented. This transform is done by viewing the sequence as a stack in Forth or Factor (first ...
  • 66.1k
12 votes
8 answers
1k views

Boustrophedon transform

Related: Boustrophedonise, Output the Euler Numbers (Maybe a new golfing opportunity?) Background Boustrophedon transform (OEIS Wiki) is a kind of transformation on integer sequences. Given a sequence ...
  • 66.1k
18 votes
4 answers
587 views

Calculate the integer square root of a matrix

Let \$A\$ be a square matrix that is at least \$2 \times 2\$ where each element is an integer. \$A^2 = A \times A\$ will then have the same dimensions as \$A\$, and will have integer elements. For ...
5 votes
5 answers
231 views

Potential nonzero entries in an irregular sequence

Background A338268 is a sequence related to a challenge by Peter Kagey. It defines a two-parameter function \$T(n,k)\$, which counts the number of integer sequences \$b_1, \cdots, b_t\$ where \$b_1 + \...
  • 66.1k
16 votes
19 answers
1k views

Compare positions of integers in this sequence

A001057 is one way to represent an integer as a natural number. It lists them according to the following pattern: 0, 1, -1, 2, -2, 3, -3, 4, -4, ... In this ...
15 votes
27 answers
3k views

Make an array of random 128 bit integers

Given an input value \$n\$, construct an array of \$n\$ random 128 bit (unsigned) integers. The integers should be uniformly random. Your code can use any in built random number generation function ...
's user avatar
8 votes
4 answers
326 views

Hexagonal section numbers

Introduction Let's draw some regular hexagons formed by hexagonal tiles, marking the vertices of the tiles with dots. Then we will count the number of dots. ...
  • 66.1k
22 votes
22 answers
3k views

Longest Zero Sum Sub-array

Given an array of integers. Find out its longest sub-array (contiguous subsequence) whose sum is 0. The sub-array for output may be an empty array. Input Input an array of integers. Output Output the ...
  • 30.8k
5 votes
3 answers
156 views

Is this an ordinal transform? [duplicate]

Related: What's my telephone number? which asks to calculate the terms of A000085, the number of possible ordinal transforms of length n. Background Ordinal transform is a transformation on an integer ...
  • 66.1k
39 votes
15 answers
2k views

Maximum number of squares touched by a line segment

Consider a square grid on the plane, with unit spacing. A line segment of integer length \$L\$ is dropped at an arbitrary position with arbitrary orientation. The segment is said to "touch" ...
  • 100k
32 votes
43 answers
3k views

Is this a Permutation of 1..n

Input a non-empty array with \$n\$ positive integers. Test if the input array contains every integer in \$1\cdots n\$. In case you prefer 0-indexed numbers, you may choose to input an array of non-...
  • 30.8k
27 votes
17 answers
3k views

Give me odd, even, square, cube, prime and composite 3-digit numbers

Given a string which is guaranteed to be either odd, even, square, ...
  • 170k
19 votes
21 answers
1k views

Binomial transform

Background Binomial transform is a transform on a finite or infinite integer sequence, which yields another integer sequence. The binomial transform of a sequence \$\{a_n\}\$ is given by $$s_n = \sum_{...
  • 66.1k
29 votes
22 answers
2k views

Consecutive Distance Rating

We'll call the consecutive distance rating of an integer sequence the sum of the distances between consecutive integers. Consider 2 9 3 6 8 1. ...
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